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Sullivan's Minimal Models and Higher Order Whitehead Products

  • Peter Andrews (a1) and Martin Arkowitz (a2)

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The theory of minimal models, as developed by Sullivan [6; 8; 16] gives a method of computing the rational homotopy groups of a space X (that is, the homotopy groups of X tensored with the additive group of rationals Q). One associates to X a free, differential, graded-commutative lgebra , over Q, called the minimal model of X, from which one can read off the rational homotopy groups of X.

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Copyright

COPYRIGHT: © Canadian Mathematical Society 1978

References

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1. Arkowitz, M., Whitehead products as images of Pontrjagin products, Trans. Amer. Math. Soc. 158 (1971), 453–463.
2. Arkowitz, M., Localization and H-spaces, Aarhus Universitet Mathematisk Institut, Lecture Notes Series No. 44 (1976).
3. Arkowitz, M. and Curjel, C. R., Zum Begriff der H-Raumes mod j∼ ‘ , Archiv der Math. 16 (1965), 186–190.
4. Barry, J., Higher order Whitehead products and fibred Whitehead products, Thesis, Dartmouth College (1972).
5. Bourbaki, N., Elements of mathematics. Algebra I, Chapters 1–3 (Hermann/Addison- Wesley).
6. Deligne, P., Griffiths, P., Morgan, J., and Sullivan, D., Real homotopy theory of Kahler manifolds, Invent. Math. 29 (1975), 245–274.
7. Dold, A., Lectures on algebraic topology (Springer-Verlag, 1972).
8. Friedlander, E., Griffith, P. and Morgan, J., Homotopy theory and differential forms, Seminario di Geometria 1972, (Firenze).
9. Hilton, P., Mislin, H. and Roitberg, J., Localization of nil potent groups and spaces, Notas de Mathematica 15 (North Holland/American Elsevier, 1975).
10. Hu, S., Homotopy theory (Academic Press, 1959).
11. Marcus, M. and Mine, H., Introduction to linear algebra (Macmillan, 1965).
12. Porter, G., Higher order Whitehead products, Thesis, Cornell University (1963).
13. Porter, G., Higher order Whitehead products, Topology 3 (1965), 123–136.
14. Porter, G., Higher order Whitehead products and Postnikov systems, Illinois J. Math. 11 (1967), 414–416.
15. Spanier, E., Algebraic topology (McGraw-Hill, 1966).
16. Sullivan, D., Differential forms and topology of manifolds, Conference on Manifolds, Tokyo (1973), 31–43.
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  • Cited by 12

  • Access

Sullivan's Minimal Models and Higher Order Whitehead Products

  • Peter Andrews (a1) and Martin Arkowitz (a2)

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